The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-p-value-state-any-key-formula-b1e1

stable pending witness
2026-05-29 06:54:51 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a p-value. State any key formula.
59 chars

Generation

A p-value is the probability of obtaining results as extreme as or more extreme than those observed, assuming the null hypothesis is true. It quantifies the strength of evidence against the null hypothesis—smaller p-values suggest stronger evidence against it. The key formula is: **p-value = P(test statistic ≥ observed value | H₀ is true)** If the p-value is less than a predetermined significance level α (commonly 0.05), we reject the null hypothesis.
26 tokens in · 109 tokens out · 2587 ms · $0.0017

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
2593.5 ms
Base LLM
2586.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0017

Trail

06:54:51 received prompt_chars=59 verifiers=['scripture_anchors', 'theology_doctrine']
06:54:51 red_gate decision=pass reason=no disqualifying input patterns detected
06:54:54 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=109 latency_ms=2586.8 cost_usd=0.0017
06:54:54 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:54:54 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:54:54 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:54:54 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:54:54 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:54:54 signed hash_algo=sha256 hash=sha256:669717d1d4019e3f46f68bc4ef10895f55d87b226224aecb290ed7999a206e3f

Content hash

sha256:669717d1d4019e3f46f68bc4ef10895f55d87b226224aecb290ed7999a206e3f

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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